Convergence and Equivalence Results for the Jensen's Inequality—Application to Time-Delay and Sampled-Data Systems

@article{Briat2011ConvergenceAE,
  title={Convergence and Equivalence Results for the Jensen's Inequality—Application to Time-Delay and Sampled-Data Systems},
  author={Corentin Briat},
  journal={IEEE Transactions on Automatic Control},
  year={2011},
  volume={56},
  pages={1660-1665}
}
The Jensen's inequality plays a crucial role in the analysis of time-delay and sampled-data systems. Its conservatism is studied through the use of the Grüss Inequality. It has been reported in the literature that fragmentation (or partitioning) schemes allow to empirically improve the results. We prove here that the Jensen's gap can be made arbitrarily small provided that the order of uniform fragmentation is chosen sufficiently large. Nonuniform fragmentation schemes are also shown to speed… CONTINUE READING
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